10. The picture shows the line with equation x+y=9 and the curve with equation y=x^2-12x+37.
The line and the curve intersect at the points P and Q and the minimum point on the curve is M, whose coordinates are (6,1).
(a) Find, using algebra, the coordinates of P and Q.
(b) Prove that triangle MPQ is right-angled.
11. Solve the simultaneous equations
x-2y+2=0
x^2-2xy+y^2=16
9. Find the set of values of x for which x^2-3x-4>0.
8. A quadratic function is defined by f(x)=x^2+8x+10.
(a)Find the values of a and b such that f(x)=(x+a)^2+b.
(b)Hence find the value of x for which f(x) has a minimum value and states its minimum value.
7.Differentiate: 3x^3+ 10x^1/2+ (4x^2+ 4x) / x^2
6.The equation x^2+ 4kx+ 4k= 0, where k is a constant, has real roots. Prove that k(16k-16)> or =0.
5.Given that 4^x=16^y-4, show that x=2y-8.
4.The points A (4,-5), B (-1,-3) and C (-5,-20.25) are the vertices of the triangle ABC and D is the midpoint of AB.
(a) Show that CD is perpendicular to AB.
(b) Find an equation of the line passing through A and b in the form ax+by=c,where a, b and c are integers to be found.
2.Calculate ∑24r=1(6 + 5r) (By the way, 24 is on the top of the sigma, r=1 is on the bottom.)
3.Find ∫(5x+ 12√x)dx
1. A sequence U1,U2,U3......is defined by
U1=10
Un+1=0.9+U1
(a)Find the valus of U4
(b)Find an expression of Un in terms of n.
(c)Find
The line and the curve intersect at the points P and Q and the minimum point on the curve is M, whose coordinates are (6,1).
(a) Find, using algebra, the coordinates of P and Q.
(b) Prove that triangle MPQ is right-angled.
11. Solve the simultaneous equations
x-2y+2=0
x^2-2xy+y^2=16
9. Find the set of values of x for which x^2-3x-4>0.
8. A quadratic function is defined by f(x)=x^2+8x+10.
(a)Find the values of a and b such that f(x)=(x+a)^2+b.
(b)Hence find the value of x for which f(x) has a minimum value and states its minimum value.
7.Differentiate: 3x^3+ 10x^1/2+ (4x^2+ 4x) / x^2
6.The equation x^2+ 4kx+ 4k= 0, where k is a constant, has real roots. Prove that k(16k-16)> or =0.
5.Given that 4^x=16^y-4, show that x=2y-8.
4.The points A (4,-5), B (-1,-3) and C (-5,-20.25) are the vertices of the triangle ABC and D is the midpoint of AB.
(a) Show that CD is perpendicular to AB.
(b) Find an equation of the line passing through A and b in the form ax+by=c,where a, b and c are integers to be found.
2.Calculate ∑24r=1(6 + 5r) (By the way, 24 is on the top of the sigma, r=1 is on the bottom.)
3.Find ∫(5x+ 12√x)dx
1. A sequence U1,U2,U3......is defined by
U1=10
Un+1=0.9+U1
(a)Find the valus of U4
(b)Find an expression of Un in terms of n.
(c)Find